Answer:
[tex]y=\dfrac{3}{2}\cdot 2^x[/tex]
Step-by-step explanation:
The general equation of the exponential function is
[tex]y=a\cdot b^x[/tex]
If the graph of the exponential function passes through the points (-2, 0.375) and (7, 192), then their coordinates satisfy the equation:
[tex]0.375=a\cdot b^{-2}\\ \\192=a\cdot b^7[/tex]
Divide the second equation by the first:
[tex]\dfrac{192}{0.375}=\dfrac{a\cdot b^7}{a\cdot b^{-2}}=\dfrac{b^7}{b^{-2}}\\ \\512=b^9\\ \\b=\sqrt[9]{512}=2[/tex]
Substitute it into the second equation:
[tex]192=a\cdot 2^7\\ \\192=a\cdot 128\\ \\a=\dfrac{192}{128}=\dfrac{96}{64}=\dfrac{48}{32}=\dfrac{6}{4}=\dfrac{3}{2}[/tex]
So, the equation of the exponential function is
[tex]y=\dfrac{3}{2}\cdot 2^x[/tex]
Khaled and Wilma were asked to find an explicit formula for the sequence 1, 3, 9, 27. Khaled said the formula is f(n)=1*3^n-1 and Wilma said the formula is f(n)=1*3^n. Which one of them is right?
ANSWER
[tex]f(n) = 1 \times ( {3}^{n - 1} )[/tex]
EXPLANATION
The given sequence is 1, 3, 9, 27...
The first term of this sequence is
[tex]a = 1[/tex]
The common ratio is
[tex]r = \frac{3}{1} = \frac{9}{3} = \frac{27}{9} = 3[/tex]
The explicit formula for this geometric sequence is
[tex]f(n) = a ( {r}^{n - 1} )[/tex]
We substitute the first term and the common ratio to obtain,
[tex]f(n) = 1 ( {3}^{n - 1} )[/tex]
Answer:
khaled is correct. f(n)=1x3^n-1
Step-by-step explanation:
Which point is located at (4,-5)?
1. A
2. B
3. C
4. D
Answer:
it is C
Step-by-step explanation:
can someone help me with this
Answer:
19 m
Step-by-step explanation:
This is Geometric progression with
[tex]\left \{ {{u_1=1,\: u_2 =2} \atop {u_n=2^{n-1}u_1} \right.[/tex]
Then the fomular of sum is
[tex]S=u_1\frac{2^n-1}{2-1} =1\times(2^n-1)=2^n-1\\To\: save\: 1 \:million\: then \; our \:sum \: will \: be\: 1000000\\Hence,\\2^n-1=1000000\\2^n=1000001\\n=log_{2}{1000001}\approx19,9\\Thus, it\:would \;be \:19 \:months \:before\: we\: saved \:1000000 \:pounds[/tex]
PLS HELP I'LL GIVE BRAINLIEST
Answer:
$5,000
Step-by-step explanation:
Create a proportion:
11/100 = 550/x
100(550)/11
5,000= x
You have to form a proportion: [tex]\frac{part}{whole}[/tex]
Meals are only 11% for the vacation budget. This means that meals would go over 100% like this:
[tex]\frac{11}{100}[/tex]
You also know that you have $550 for meal (your part) but you want to know what your total vacation budget is(your whole)[tex]\frac{x}{550}[/tex] (x), so you would set it up like this
Now you sent them equal to solve for x:
[tex]\frac{11}{100} = [tex]\frac{550}{x}[/tex]
cross multiply:
11x = 55,000
x = 5,000
This means that your total vacation budget is $5,000
Hope this helped!
I could probably figure this out but I have way too much homework so It'd be nice to finish this pathway.
Yeah that's right always be a hardworking person
Mrs. Piper is driving Anna, Jo, and Mai home from school. All of them want to ride in the front seat. How can she make a fair decision about who rides in the front seat?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The question is on probability
We have three students, Anna, Jo and Mai
We have 1 seat at the front
P(S)=3
P(A)=1/3
P(J)=1/3
P(M)=1/3
A tessellation is an arrangement of repeating shapes that have what
characteristic?
Answer:
Option B is correct, (no spaces or overlaps exist between it's pieces).- APEX
Step-by-step explanation:
I hope this helps.
Answer: No spaces or overlaps exist between its pieces.
At midnight, the temperature outside is 8 degrees Celsius. The forecast calls for the temperature to drop by 1.5 degrees Celsius per hour. At what time will the temperature reach 0 degrees Celsius?
Answer:
It will reach 0 degrees celcius at 5:20AM i believ
Step-by-step explanation:
If you divide 8 by 1.5 you bet 5 and 1/3
5 1/3 turns to 5:20 AM
Mathematics probability
Do you have a specific question or something like that which you need answering?
A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = (x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.
y = x +
3y = –4x + 40
4x + y = 21
4x + 3y = 5
–4x + 3y = 17
Answer:
3y+4x=5
Step-by-step explanation:
step 1
Find the slope
we have
(–7, 11) and (8, –9)
m=(-9-11)/(8+7)
m=-20/15
m=-4/3
step 2
Find the equation of the line into point slope form
we have
m=-4/3
point (-7,11)
substitute
y-11=-(4/3)(x+7) ----> equation of the line into point slope form
Multiply by 3 both sides
3y-33=-4(x+7)
3y-33=-4x-28
3y+4x=33-28
3y+4x=5 -----> equation of the line into standard form
Answer:
The first and 4th option
Step-by-step explanation:
Just took it on edge
Angelica swims 14 3/7 hours per month. If she swims the same amount every month, how many hours does she swim in 6 months?
85 4/7 hours
86 1/7 hours
86 4/7 hours
86 1/7 hours
Answer:
86 4/7, C.
Step-by-step explanation:
14x6= 84
+
6 x 3/7 = 2 4/7
86 4/7
Answer:
multiply 14 over 7 to get the number as one fraction. after adding three to that product, you get 101/7. Multiply that by 6/1 to get 606/7, then divide 606 by 7 to get 86 4/7 hours every 6 months.
Step-by-step explanation:
A circuit contains three resistors rated at 100 Ω, 200 Ω, and 300 Ω that are connected in parallel. What's the total resistance of the circuit?
Answer:
total resistance is 54.54 ohms
Step-by-step explanation:
In parallel circuits, current can take various paths so the resistance are not added simply like that in series circuit, instead the reciprocal of total resistance in parallel circuit is calculated by adding the reciprocals of all the resistors connected parallel in circuit.
Given:
Resistor r1= 100
resistor r2 = 200
resistor r3= 300
The three resistors are connected in parallel so the total resistance will be calculated by:
1/R= 1/r1 +1/r2 +1/r3
Putting the values of r1, r2, r3 in above we get
1/R= 1/100 + 1/200 +1/300
= 0.01 + 0.005 + 0.0033
= 0.0183
Taking reciprocal of both sides:
R=54.54
Hence total resistance is 54.54 ohms!
Final answer:
The total resistance of three resistors rated at 100 Ω, 200 Ω, and 300 Ω connected in parallel is approximately 54.64 Ω. This is calculated using the reciprocal formula for parallel resistances.
Explanation:
When you have a circuit with resistors connected in parallel, the total (or equivalent) resistance of the circuit is found by using the reciprocal formula:
Rtotal = 1/(1/R1 + 1/R2 + 1/R3)
For the given resistors of 100 Ω, 200 Ω, and 300 Ω in parallel, you calculate the total resistance like this:
Rtotal = 1/(1/100 Ω + 1/200 Ω + 1/300 Ω)
= 1/(0.01 Ω-1 + 0.005 Ω-1 + 0.0033 Ω-1)
= 1/(0.0183 Ω-1)
= 54.64 Ω
The total resistance of the circuit would therefore be approximately 54.64 Ω.
Simplify the following expression.
A. 64
B. 12
C. 1/12
D. 1/64
We have
[tex]a^b\cdot a^c=a^{b+c}[/tex]
[tex]a^b\div a^c=a^{b-c}[/tex]
So, in your case, we have
[tex]4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}} = 4^{-\frac{11}{3}+\frac{2}{3}} = 4^{-\frac{9}{3}}=4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}[/tex]
Answer:
Option D. 1/64
Step-by-step explanation:
We have to simplify the following expression
[tex]4^{-\frac{11}{3} }[/tex] ÷ [tex]4^{-\frac{2}{3} }[/tex]
= [tex]\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }[/tex]
= [tex][4^{-\frac{11}{3}}[/tex] × [tex]4^{\frac{2}{3}}][/tex] [since [tex]\frac{1}{A-1}[/tex]=a]
= [tex]4^{(-\frac{11}{3}+\frac{2}{3})}[/tex] [since [tex]a^{b}[/tex] × [tex]a^{c}[/tex] = [tex]a^{(b+c)}[/tex]]
= [tex]4^{-\frac{9}{3}}[/tex]
= [tex]4^{-3}[/tex]
= [tex]\frac{1}{4^{3} }[/tex] [[tex]a^{-1}=\frac{1}{a}[/tex]]
= [tex]\frac{1}{64}[/tex]
Option D. 1/64 is the answer.
Select the two figures that are similar to each other.
Answer:
B and D
Step-by-step explanation:
if they had letters it would be
A B
C D
options B and D are similar
Answer:
II and IV
Step-by-step explanation:
We are given that four figures
We have to find two similar figures.
Similar figures: Two triangle are called similar when the ratio of corresponding sides are equal and corresponding angles are equal.
In Second and fourth figure
Each angle of second figure is equal to its corresponding angle of fourth figure.
Ratio of corresponding sides
[tex]\frac{6}{12}=\frac{1}{2}[/tex]
[tex]\frac{2.5}{5}=\frac{1}{2}[/tex]
[tex]\frac{6.5}{13}=\frac{1}{2}[/tex]
[tex]\frac{6}{12}=\frac{2.5}{5}=\frac{6.5}{13}[/tex]
Hence, second and fourth figure are similar to each other.
A container holds 9 red markers, 13 blue markers, and 17 green markers. You will randomly select two markers without replacement.
a.) Fill in the probabilities on each branch of the tree diagram. Use the boxes with the fraction bars already provided.
b.) Use the tree diagram to answer the following:
• How many ways can you select the markers?
• How many ways can you select exactly 1 blue marker?
• What is the probability that you select 2 red markers?
• What is the probability that you select a green marker and then a red marker?
Answer:
a.
R-------8/38--------RR
R------9/39--------B-------13/38-------RB
G------17/38--------RG
R-------9/38--------BR
B--------13/39------B-------12/38-------BB
G-------17/38-------BG
R-----9/38--------GR
G---------17/39-------B------13/38-------GB
G------16/38-------GG
b).
9 waysways you can select 1 blue are; RB,BR,BG,GBRB=9/39 × 13/38=3/38
BR= 13/39 × 9/38 =3/38
BG= 13/39 × 17/38=17/114
GB= 17/39 × 13/38=17/114
=3/38 +3/38+17/114+ 17/114 =26/57
Probability of selecting 2 red markers= RR = 9/39 × 8/38 =12/247Probability of selecting a green marker and then a red marker= GR= 17/39×9/38 =51/494What is (u+2ax)(2u+2ax)
Answer:
2u^2 +6aux+4ax
Step-by-step explanation:
2u^2 because u×2u
2aux cuz u× 2ax
4aux cuz 2ax×2u
4ax. cuz 2ax time 2ax
The multiplication of the binomials (u+2ax)(2u+2ax) can be solved using the FOIL method. The steps result in 2u^2 + 2uax + 4uax + 4a^2x^2. Combining like terms yields the final answer: 2u^2 + 6uax + 4a^2x^2.
Explanation:The problem (u+2ax)(2u+2ax) is a mathematical multiplication of two binomial expressions. You may solve it by applying the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Let's walk through the steps to solve it:
First: Multiply the first terms in each binomial. u * 2u = 2u^2. Outer: Multiply the outer terms, which are u and 2ax. u * 2ax = 2uax. Inner: Multiply the inner terms, which are 2ax and 2u. 2ax * 2u = 4uax. Last: Multiply the last terms of each binomial. 2ax * 2ax = 4a^2x^2.Then, add these results together: 2u^2 + 2uax + 4uax + 4a^2x^2. Combine like terms to get the final answer: 2u^2 + 6uax + 4a^2x^2.
Learn more about Binomial multiplication here:https://brainly.com/question/35831420
#SPJ2
A customer wants you to enlarge a photo to 2 3/4 its current height. The photo’s current height is 3 1/4 inches. What should its enlarged height be, in inches?
Answer:
8 15/16 inches
Step-by-step explanation:
Multiply 3 1/4 inches by 2 3/4:
13 11
---- * ----- = 146/16 inches, or 8.9375 inches, or 8 15/16 inches.
4 4
Answer: The required enlarged height of the photo is [tex]8\dfrac{15}{16}~\textup{inches}.[/tex]
Step-by-step explanation: Given that a customer wants you to enlarge a photo to [tex]2\dfrac{3}{4}[/tex] its current height and the photo’s current height is [tex]3\dfrac{1}{4}[/tex] inches.
We are to find the enlarged height of the photo in inches.
The enlarged height of the photo is given by
[tex]2\dfrac{3}{4}\times \textup{current height of the photo}\\\\\\=\dfrac{11}{4}\times3\dfrac{1}{4}\\\\\\=\dfrac{11}{4}\times\dfrac{13}{4}\\\\\\=\dfrac{143}{16}\\\\=8\dfrac{15}{16}.[/tex]
Thus, the required enlarged height of the photo is [tex]8\dfrac{15}{16}~\textup{inches}.[/tex]
need help asap!!!!! thank you!!
Answer:
1,2,20
take away 14 from 8 = 6
add 6 to 14 = 20
Hope I helped!
NOTE: MARK BRAINLIEST!!!! plz....
Answer:
8,4
14,7
6,3
Step-by-step explanation:
if the length of side of square is 3x-y,what is the area of the square in terms of x.and y?
Answer:
[tex]\large\boxed{A=9x^2-6xy+y^2}[/tex]
Step-by-step explanation:
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side length
We have s = 3x - y. substitute:
[tex]A=(3x-y)^2[/tex] use (a - b)² = a² - 2ab + b²
[tex]A=(3x)^2-(2)(3x)(y)+y^2=9x^2-6xy+y^2[/tex]
Would appreciate the help.
Answer:
[tex]x^{2}+(y+2)^{2}=9[/tex]
Step-by-step explanation:
The center of the circle is (0, -2). The dark-filled circle is the center and lies 2 units below the origin on the y-axis.
On the other hand, the radius of the circle is 3 units. If we count from the dark-filled circle, we have 3 complete squares to the left, to the right.
Now the standard equation of a circle with center (a, b) and radius r units is given by the formula;
[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]
Substituting the values obtained;
[tex]x^{2}+(y+2)^{2}=9[/tex]
and is our standard equation of the given circle
Solve Applications involving Uniform Motion
Question
Lorena walks the path around the park in 30 minutes. If she jogs, it takes her 20 minutes. Her jogging speed is 2 miles per
hour faster than her walking speed. Find Lorena's walking speed and jogging speed.
Answer:
6mph and 4mph
Step-by-step explanation:
because 2:3 is some as 3x:x in terms of speed
Answer: The speed of her walking is 4 mph and the speed of her jogging is 6 mph.
Step-by-step explanation:
Since we have given that
Time taken by Lorena to walk the path = 30 minutes
Time taken by Loren to jogs the path = 20 minutes
Let the speed of her walking be 'x'.
Let the speed of her jogging be 'x+2'.
Since distance would remain same, so it becomes,
[tex]30x=20(x+2)\\\\30x=20x+40\\\\30x-20x=40\\\\10x=40\\\\x=\dfrac{40}{10}\\\\x=4\ mph[/tex]
Hence, the speed of her walking is 4 mph and the speed of her jogging is 6 mph.
Bobby-Joe takes a 25-question test for which he receives 4 points for each correct answer and loses 1 point for each wrong answer. If Bobby-Joe answers all the questions and gets a passing grade of 65%, how many questions did he get right?
Answer:
Let x be the number of questions he gets right. Let y be the number of questions he gets wrong.
Then:
x + y = 25
4x - 1y = 65
Adding these two equations gives:
5x = 90
x = 90/5 = 18 right answersy = 25 - 18 = 7 wrong answers
* Hopefully this helps:) Mark me the brainliest:)!!!
~ 234483279c20~
The number of right questions is 18
How to determine the right question?Let the number of right questions be x, and the wrong questions be y
So, we have the following equations
x + y = 25
4x - y = 65
Add both equations
5x =90
Divide both sides by 5
x = 18
Hence, the number of right questions is 18
Read more about system of linear equations at:
https://brainly.com/question/13729904
!!!!!PLEASE HELP!!!!
Find (f/g)(x) for: f(x)=(x+16)/x; g(x)=(2x)/(x+4)
Answer:
Step-by-step explanation:
All you have to do here is to divide polynomial f(x) = (x + 16)/x by polynomial g(x) = 2x / (x + 4), simplify the result and label the quotient properly. Recall that division by a fraction involves inverting the divisor fraction and then multiplying.
(x + 16) (x + 4) (x + 16)(x + 4)
(f/g)(x) = ------------- * ----------- = --------------------
x 2x 2x^2
Note that this quotient is true for all x except x = 0.
If a-b=2 and b=2 find the value of a×b
Answer:
a*b = 8
Step-by-step explanation:
a-b =2
Let b= 2
a-2 =2
Add 2 to each side
a-2+2 =2+2
a =4
We want to find a*b
4*2 = 8
a*b = 8
First substitute 2 in for b to get a - (2) = 2.
Now isolate a by adding 2 to both sides to get a = 4.
Since a = 4, substitute 4 in for a and 2 in for b to get 4 × 2.
Multiplying, 4 × 2 gives us a product of 8.
So the value of a × b is 8.
Select the two values of x that are roots of this equation.
x^2+1=5x
*APEX
Answer:
[tex]\large\boxed{B.\ x=\dfrac{5+\sqrt{21}}{2},\ C.\ x=\dfrac{5-\sqrt{21}}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\================================\\\\\text{We have}:\\\\x^2+1=5x\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\x^2-5x+1=0\\\\a=1,\ b=-5,\ c=1\\\\b^2-4ac=(-5)^2-4(1)(1)=25-4=21\\\\x=\dfrac{-(-5)\pm\sqrt{21}}{2(1)}=\dfrac{5\pm\sqrt{21}}{2}[/tex]
Answer:
b and c Apex answers
(HELP ASAP PLEASE)
There are two mystery numbers. The sum of 9 times the first number and 4 times the second number is 26. The sum of 3 times the first number and 4 times the second number is 14. What are the two numbers?
The first number is ___ and the second number is ___ .
Answer:
first number is 2, second number is 2
Step-by-step explanation:
If the first number is 'a' and second number is 'b'. We can use simultaneous equations
9a + 4b = 26
3a + 4b = 14
therefore by taking the second equation from the first
6a = 12
a = 2 (first number)
as a = 2
(3 x 2) + 4b = 14
6 + 4b = 14
4b = 8
b = 2 (second number)
By setting up a system of equations, we find that the two mystery numbers are both 2. This conclusion is reached by first eliminating the variable representing the second number and then solving for the first number, which turns out to be 2. Subsequently, the value of the second number is also determined to be 2.
We can solve for the two mystery numbers by setting up a system of linear equations based on the information given:
9 times the first number plus 4 times the second number equals 26.
3 times the first number plus 4 times the second number equals 14.
Let's designate the first number as x and the second number as y. Then, we can express the problem using equations:
9x + 4y = 26 (1)
3x + 4y = 14 (2)
Next, we'll solve this system of equations. We can start by subtracting equation (2) from equation (1), which will remove y from the equations, as the coefficients before y are the same:
(9x + 4y) - (3x + 4y) = 26 - 14
6x = 12
After simplifying the equation, we find that:
x = 12 / 6
x = 2
Now that we have the value for x, we can substitute it back into either (1) or (2) to find y:
9(2) + 4y = 26
18 + 4y = 26
4y = 26 - 18
4y = 8
y = 8 / 4
y = 2
Therefore, the first number is 2 and the second number is also 2.
The temperature in Chicago, Illinois, is -1°F, and the temperature in Phoenix, Arizona, is 40°F Which of the following is true?
A Chicago's temperature > Phoenix's temperature
B. Chicago's temperature < Phoenix's temperature
C. Chicago's temperature = Phoenix's temperature
Answer:
Chicago's temperature < Phoenix's temperature
Step-by-step explanation:
Because -1°F is less than 40°F.
What is the value of x?
Answer:
do you have any more information to solve this ?????????
Step-by-step explanation:
what is the actual equation it goes with??
Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete
y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
Answer:
A
Step-by-step explanation:
3/8(2x-8/3x)=21 solve the equation for x
Answer:
[tex]\boxed{\bold{x=-84}}[/tex]
Explanation:
Multiply Both Sides By 8:
= [tex]\bold{8\cdot \frac{3}{8}\left(2x-\frac{8}{3}x\right)=21\cdot \:8}[/tex]
Simplify:
= [tex]\bold{-2x=168}[/tex]
Divide Both Sides By -2:
= [tex]\bold{\frac{-2x}{-2}=\frac{168}{-2}}[/tex]
Simplify:
= [tex]\bold{x=-84}[/tex]
//Mordancy //.
X= -84 this would be your answer also use photomath :)